A solution contains 30L of pure milk. 10% of his this is taken out. Another 15% of the remaining solution is taken out and finally 20% of the contents left is taken out. The total content taken out replaced with water. Find the ratio of milk to water in the final solution.

Solution

Quantity of milk = 30L  When 10% solution is taken out = 10/100×30 = 3 L Remaining solution = 30 L – 3 L = 27 L Now, again 15% of solution is taken out = 15/100×27 = 4.05 L Remaining solution = 27 L – 4.05 L = 22.95 L Now, further 20% of solution is taken out = 20/100×22.95 = 4.59 L Remaining solution = 22.95 L – 4.59 L = 18.36 L  Total quantity taken out which is replaced by water = 30 L – 18.36 L = 11.64 L ∴ Required ratio = 11.64 : 18.36 = 582:918 =291:459 = 97:153  ALTERNATE METHOD: Quantity of Milk in final remaining mixture  = 30×(1-10/100)× (1-15/100)×(1-20/100)=30×0.9×0.85×0.8=18.36 Total quantity taken out which is replaced by water = 30 L – 18.36 L = 11.64 L ∴ Required ratio = 11.64 : 18.36 = 582:918 =291:459 = 97:153